1 Introduction

The field of gravitational-wave (GW) astronomy will soon become a reality. The first generation of
ground-based interferometric detectors (LIGO [177], VIRGO [324], GEO600 [122], TAMA300 [301]) are
beginning their search for GWs. Upgrades for two of these detectors (LIGO, VIRGO) have already begun
and in the next few years, the sensitivity of both these detectors will be increased. In addition, these two
detectors have begun working more closely together, improving their net sensitivity. After these
detectors are complete, they will have sensitivities necessary to regularly detect emissions from
astrophysical sources. New detectors, such as the Large-Scale Cryogenic Gravitational-wave
Telescope (LCGT) as well as technology developing sites such as the Australian Interferometric
Gravitational Observatory (AIGO) are also contributing to the progress in GW astronomy
(see [145] for a review). A space-based interferometric detector, LISA [182], could be launched in
the next decade. One important class of sources for these observatories is stellar gravitational
collapse. This class covers an entire spectrum of stellar masses, from the accretion-induced collapse
(AIC) of a white dwarf and the collapse of low-mass stars, including electron-capture supernovae
(), through the collapse of massive stars () that produce and the even more
massive stars () that produce the “collapsar” engine believed to power long-duration
gamma-ray bursts [333], massive and very massive Population III stars (),
and supermassive stars (SMSs, ). Some of these collapses result in explosions
(Type II, Ib/c supernovae and hypernovae) and all leave behind neutron-star or black-hole
remnants1.

Strong GWs can be emitted during a gravitational collapse/explosion and, following the collapse, by the
resulting compact remnant [309, 205, 206, 88, 269, 108, 150]. GW emission during the collapse itself may
result if the collapse or explosion involves aspherical bulk mass motion or convection. Rotational or
fragmentation instabilities encountered by the collapsing star will also produce GWs. Pulsations and
instabilities in the newly formed neutron star (a.k.a. proto neutron star) may also produce observable GWs.
Asymmetric neutrino emission can also produce a strong GW signature. Neutron-star remnants of
collapse may emit GWs due to the growth of rotational or r-mode instabilities. Black-hole
remnants will also be sources of GWs if they experience accretion-induced ringing or if the
disks around the black hole develop instabilities. All of these phenomena have the potential of
being detected by GW observatories because they involve the rapid change of dense matter
distributions.

Observation of gravitational collapse by GW detectors will provide unique information, complementary
to that derived from electromagnetic and neutrino detectors. Gravitational radiation arises from the
coherent superposition of mass motion, whereas electromagnetic emission is produced by the incoherent
superposition of radiation from electrons, atoms, and molecules. Thus, GWs carry different kinds of
information than other types of radiation. Furthermore, electromagnetic radiation interacts strongly with
matter and thus gives a view of the collapse only from lower density regions near the surface of the star, and
it is weakened by absorption as it travels to the detector. In contrast, gravitational waves can
propagate from the innermost parts of the stellar core to detectors without attenuation by
intervening matter. With their weak interaction cross-sections, neutrinos can probe the same region
probed by GWs. But whereas neutrinos are extremely sensitive to details in the microphysics
(equation of state and cross-sections), GWs are most sensitive to physics driving the mass motions
(e.g., rotation). Combined, the neutrino and the GW signals can teach us much about the
conditions in the collapsing core and ultimately the physics that governs stellar collapse (e.g.,
[7, 107, 167, 228]).

The characteristics of the GW emission from gravitational collapse have been the subject of much study.
Core-collapse supernovae, in particular, have been investigated as sources of gravitational radiation for
nearly four decades (see, e.g., [251, 311, 253, 64, 204, 89, 201, 350, 245, 106, 108, 67, 68, 165, 232]).
However, during this time research has produced estimates of GW strength that vary over orders of
magnitude. This is due to the complex nature of core collapse. Important theoretical and numerical issues
include

proper treatment of microphysics, including the use of realistic equations of state and neutrino
transport,

simulation in three-dimensions to study non-axisymmetric effects,

inclusion of general-relativistic effects,

inclusion of magnetic-field effects, and

study of the effect of an envelope on core behavior.

To date, collapse simulations generally include state-of-the-art treatments of only one or two of the
above physics issues (often because of numerical constraints). For example, those studies that
include advanced microphysics have often been run with Newtonian gravity (and approximate
evaluation of the GW emission; see, e.g., Section 4.1). Very few, if any simulations, have reached
any convergence in spatial resolution. Many of the codes have not been tested to see if their
algorithm implementations guard against standard numerical artifacts. For example, very few codes
used have tested the effects of the non-conservation of angular momentum and the numerical
transport of this angular momentum. A 3D, general relativistic collapse simulation that includes all
significant physics effects is not feasible at present. However, good progress has been made on
the majority of the issues listed above; the more recent work will be reviewed in some detail
here.

The remainder of this article is structured as follows. We first review the basic modes of GW emission in
stellar collapse presenting, where they exist, analytic formulae that have been used to estimate these GWs
(Section 2). The latter half of Section 2 presents many of the numerical approximations used to calculate
GW emission. Section 3 covers the various collapse scenarios and their GW sources: normal core-collapse
supernovae (Section 3.1), the accretion induced collapse (AIC) of a white dwarf (Section 3.2), the
collapse of low mass stars and electron capture supernovae (Section 3.3), and the collapse of
massive (Section 3.4) and supermassive (Section 3.5) stars. For each, we review the current
understanding of the occurrence rate, collapse evolution, and the specific causes behind GW
emission. Section 4 then discusses the current state of the calculations for sources arising from:
bounce (Section 4.1), convection (Section 4.2), bar modes (Section 4.3), neutrinos (Section 4.4),
r-modes (Section 4.5), fragmentation (Section 4.6), and ringing (Section 4.7). We conclude by
tying together all of these sources with their emission mechanisms to predict a complete GW
sky.

One final word of warning. In many cases, the total GW signal from stellar collapse can be tuned by
altering key initial conditions (such as the rotation rate of the collapsing star). Many of the strongest GW
estimates in the literature tend to use rotation rates that are orders of magnitude higher than that
predicted for most stars. These more optimistic results often predict that the current set of detectors should
observe GWs from astrophysical sources. In many cases, studies of these extreme conditions provide insight
into possible mechanisms for GW emission. To include these new insights, we will discuss these results in
this review. The exact nature of the initial conditions may make certain GW signals undetectable.
For each of the these scenarios, we strive to distinguish academic studies with more realistic
estimates of the signal. Our summary is based on what we judge to be the more realistic signal
predictions.